Around 6,000 refugees from the persecuted minority have been camping on the narrow stretch of land since fleeing a brutal military crackdown in Myanmar's west last August.
The majority of the nearly 700,000 Rohingya who escaped the violence settled in huge camps in Bangladesh but a smaller number insisted on staying put in the buffer zone between the borders.
Myanmar had agreed in February to stop using loudspeakers to order the stranded Muslims to leave the area immediately and cross into Bangladesh.
The army also withdrew some of its heavy forces from the edge of no-man's land, where refugees camped on the other side of a barbed wire fence had complained of intimidation.
But the loudspeaker messages resumed this weekend without warning, Rohingya community leaders said, exacerbating tension along the restive border zone.
"They played it several times yesterday, and have been repeating it this morning. It's very disturbing and creates panic," said Mohammad Arif, one of the leaders camped in no-man's land.
The messages - broadcast in Burmese and Rohingya - warned the refugees to "leave the area under Myanmar's jurisdiction or face prosecution".
"We're citizens of Myanmar. It's our fatherland. We have every right to remain here. Why should we go elsewhere?" said another community leader, Dil Mohammad.
The broadcasts also refer to the refugees as "Bengalis", the term used by many in Buddhist-majority Myanmar to refer to the Rohingya, whom they consider interlopers from Bangladesh.
Lieutenant Colonel Manzurul Hasan Khan, a local Border Guard Bangladesh commander, said the situation was being closely monitored.
"We have noticed that they tied loudhailers to the trees along their border fences near the camp," Khan said.
The refugee crisis has strained ties between Bangladesh and Myanmar.
The neighbours had agreed in November to begin repatriating Rohingya refugees to Myanmar but the process has stalled, with both sides blaming each other for the delays.
Those living in no-man's land - and many in the Bangladeshi refugee camps - refuse to return to Myanmar until their safety and citizenship is assured and compensation granted for past injustices.
